by
Kaufmann, Jerome; Schwitters, Karen;

Answer

{$-2,0,2$}

Work Step by Step

Since $2x$ is common to both the terms of the equation, we take it out as a common factor:
$2x^{3}-8x=0$
$2x(x^{2}-4)=0$
We simplify the expression further using the rule $a^{2}-b^{2}=(a+b)(a-b)$:
$2x(x^{2}-4)=0$
$2x(x^{2}-2^{2})=0$
$2x(x+2)(x-2)=0$
Now, we equate all the factors to zero to solve the equation:
$2x(x+2)(x-2)=0$
$2x=0$ or $(x+2)=0$ or $(x-2)=0$
$x=0$ or $x=-2$ or $x=2$
Therefore, the solution set is {$-2,0,2$}.